1. Field of the Invention
The present invention relates to a method of arranging signal points on a complex plane in a quadrature amplitude modulation/demodulation system and a quadrature amplitude modulator/demodulator device using this method.
2. Description of the Related Art
Recently, various types of high-speed modems which modulate and transmit digital signals at high speed have been manufactured as significant improvements have been made in the processing power of digital-signal processing LSIs. In order to implement high-quality data transmission using high-speed modems, it is essential to introduce a modulation/demodulation system which is capable of maximizing the signal-to-noise (S/N) ratio while minimizing transmission error rate.
To provide efficient communication, the quadrature amplitude modulation/demodulation system is adapted to transmit as much digital data as possible within a limited transmission bandwidth. In this system, a correspondence is established between M kinds of data patterns represented by log.sub.2 M bits and M signal points on a complex plane. Two carrier components cos.sub..omega. t and sin.sub.107 t (.sub..omega. is angular frequency of carriers and t is time), which are 90.degree. apart in phase, are amplitude modulated with a real value and an imaginary value, respectively, indicating coordinate data of each signal point on the complex plane. The resulting amplitude modulated carriers are added to produce a combined modulated signal for transmission. On the other hand, the demodulation side multiplies the modulated signal by sin .sub..omega. t and cos.sub..omega. t to extract the real value and the imaginary values. A corresponding one of the M signal points is identified by these values so that M kinds of data patterns are demodulated.
In this case, parameters such as the S/N ratio and transmission error rate of a data transmission device, depend upon the way signal points are arranged on the complex plane. In general, to implement a signal point arrangement for achieving good transmission performance, two conditions should be satisfied.
First, the transmission error rate depends on the distance between signal points on the complex plane. That is, where a signal point is identified by a modulated signal in the demodulation system, if the distance between signal points is too small on the complex plane, a signal point adjacent to the true signal point may be extracted erroneously. To secure a low transmission error rate, therefore, the distance between each pair of signal points on the complex plane must be accurately determined. In particular, in order to secure a low, constant transmission error rate among signal points, the distance between adjoining signal points should be constant.
Second, in general, when a transmitter is supplied with high-power modulated signals, its output is liable to saturate, thus increasing transmission error. The power of modulated signals must therefore be made as low as possible so as to decrease transmission power. The peak power of modulated signals in particular must be made as low as possible. It is known that the power of a modulated signal based on a signal point on the complex plane is proportional to the square of the distance between the signal point and the origin of the complex plane. It is also known that the farther a signal point is from the origin, the higher is the power of a modulated signal corresponding to that signal point. In order to lower the power of modulated signals, therefore, it is required to arrange each signal point as close to the origin as possible.
A conventional method of arranging signal points in a quadrature amplitude modulator/demodulator device is described below, taking the above two conditions into consideration.
A first prior art signal point arranging method, is shown in FIG. 1A. Here, signal points are arranged in an 8.times.8 grid-like pattern on a phase plane with an outward form of a square. A second prior art, signal point arranging method is shown in FIG. 1B. Here, four corners of a square are cut away. According to both of these prior art methods, the distance between signal points can be made constant, thus meeting the first condition. There is also an integral-multiple relationship in each of the real and imaginary values in coordinate data between signal points, thus permitting such modulator/demodulator devices to be simply constructed. In both the first and second prior arts, however, no measures are taken to bring the signal points as close to the origin of the complex plane as possible, thus failing to meet the above second condition. Therefore, a problem arises in that the peak power of modulated signals cannot be made sufficiently low, thus making the transmission error rate high.
Next, as a third prior art, there is known a signal point arranging method, which is disclosed in published examined Japanese Patent Application No. 63-24342. Here, signal points located at corners distant from the coordinate axes of the complex plane are relocated close to the coordinate axes, thereby decreasing signal transmission power. With the third prior art, however, there is no diagrammatic regularity for relocating signal points on the complex plane. When the number of signal points is increased, they have to be relocated by trial and error, thus making the process troublesome.
As a fourth prior art, there is known a signal point arranging method, which is disclosed in published unexamined Japanese Patent Application No. 60-150359. Here, signal points are arranged on concentric circles disposed at equal intervals and in this case the signal points are determined so that the distance between them may have almost a predetermined value. In the case of this prior art, each signal point is arranged so that it may be brought as close as possible to the origin of the complex plane, thus complying with the above second condition. With the fourth prior art, however, signal points have to be positioned on each of the concentric circles by trial and error so that the distance between the signal points may be equal to or more than the predetermined value, thus making the logic for the signal point arrangement very difficult. In particular, it is necessary to measure and evaluate the distance between signal points each time a signal point is arranged. As can be seen, a problem with the fourth prior art is that the arrangement of signal points cannot be determined readily.